Binary_Offset_Carrier_(BOC)

Binary Offset Carrier Signals are a particular case of BCS signals with a representation vector formed by +1’s and -1’s alternating in a particular defined way. Two notations [E. Rebeyrol et al., 2005] ^[1] can be found in the literature to define the BOC signals. We describe them shortly in the following lines.

The first model defines the BOC modulation as the result of multiplying the PRN code with a sub-carrier which is equal to the sign of a sine or a cosine waveform, yielding so-called sine-phased or cosine-phased BOC signals respectively as shown in [J.W. Betz, 2001] ^[2], [L.R.Weill, 2003] ^[3], [J. Godet, 2001] ^[4] and [E. Rebeyrol et al., 2005] ^[1]. According to this definition, the expression of the sine-phased BOC signal would be:

with

where

• c_k is the code sequence waveform,
• f_s is the sub-carrier frequency,
• and is the Non Return to Zero (NRZ) code materialization with value 1 over the support .

The second model defines the BOC modulation as follows:

where describes the chip waveform and is broken up into n rectangular pulses of duration T_c / n with amplitude ±1. It is important to note that in this case the sine-phasing or cosine-phasing is considered as part of the chip waveform definition. This convention has been introduced in [A.R. Pratt and J.I.R. Owen, 2003a] ^[5] and [J.W. Betz, 2001]^[2].

No matter what definition we choose to describe the BOC modulation in the time domain, the BOC signal is commonly referred to as BOC(fs, fc) where and so that generally one only says BOC(m, n) for simplicity. Moreover, unless it is indicated in a different way, when we talk about BOC signals we will always mean the sine-phased variant.

 

 

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